# Quantum Error Correction & Fault Tolerance Domain: Quantum Computing & Information · 279 papers indexed · newest 2026-10-27 Surface codes and qLDPC codes, below-threshold logical qubits, real-time decoding, magic-state distillation and cultivation, and resource estimates for fault tolerance. Key concepts: quantum error correction, surface code, fault-tolerant, logical qubit, qLDPC, below threshold, magic state, decoder ## Research dossier (premium) **Quantum Error Correction & Fault Tolerance: State of the Field (October 2026)** (v1, updated 2026-10-29; 6,183 words, 90 sources, 40 evidence-mapped claims) An expert briefing on quantum error correction as of late October 2026: surface, color and qLDPC codes, bosonic and erasure qubits, real-time decoding, magic-state preparation and fault-tolerant resource estimates. The main takeaway is that below-threshold error suppression has been shown on superconducting hardware, in a short neutral-atom surface-code circuit and, in a 2026 preprint, in trapped-ion color-code memories, so the bottleneck has shifted to logical gates, magic-state cost, decoding latency, correlated errors and scale. Published estimates for factoring RSA-2048 have fallen from 20 million noisy qubits (2019) to under one million (2025); 2026 preprints claim under 100,000 with qLDPC codes, and Shor's algorithm at cryptographically relevant scale on as few as 10,000 reconfigurable atoms, with runtime falling as qubits are added, all assuming hardware not yet demonstrated at scale. - Preview (free): https://space-kitty.com/api/v1/dossiers/quantum-error-correction/preview - Full dossier ($0.20 via x402): https://space-kitty.com/api/v1/dossiers/quantum-error-correction - Research pack ($0.20): https://space-kitty.com/api/v1/topics/quantum-error-correction/pack ## Most influential - **[Logical quantum processor based on reconfigurable atom arrays](https://space-kitty.com/papers/arxiv:2312.03982)**. Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim et al. · 2023 · Nature (arXiv:2312.03982 · doi:10.1038/s41586-023-06927-3 · 1,118 citations). Source: > Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected \`\`logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, ou… - **[Suppressing quantum errors by scaling a surface code logical qubit](https://space-kitty.com/papers/arxiv:2207.06431)**. Google Quantum AI, Rajeev Acharya, I. L. Aleǐner et al. · 2023 · Nature (arXiv:2207.06431 · doi:10.1038/s41586-022-05434-1 · 1,102 citations). Source: > Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance … - **[Superconducting quantum circuits at the surface code threshold for fault tolerance](https://space-kitty.com/papers/arxiv:1402.4848)**. R. Barends, J. Kelly, A. Megrant et al. · 2014 · Nature (arXiv:1402.4848 · doi:10.1038/nature13171 · 1,741 citations). Source: > A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-… - **[Quantum error correction below the surface code threshold](https://space-kitty.com/papers/arxiv:2408.13687)**. Rajeev Acharya, Laleh Aghababaie-Beni, Igor Aleiner et al. · 2024 · Nature 638 (2025) 920-926 (arXiv:2408.13687 · doi:10.1038/s41586-024-08449-y · 774 citations). Source: > Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $Λ$ = 2.14 $\\pm$ 0.02 when inc… - **[How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits](https://space-kitty.com/papers/arxiv:1905.09749)**. Craig Gidney, Martin Ekerå · 2021 · Quantum (arXiv:1905.09749 · doi:10.22331/q-2021-04-15-433 · 829 citations). Source: > We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekerå-Håstad 2017, Ekerå 2017, Ekerå 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for large-scale superconducting qubit platforms: a planar grid of qubits with nearest-neighbor connectivity, a characteristic physical gate error rate of $10^{-3}$, a surface code cycle time of 1 microsecond, and a reacti… - **[Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code](https://space-kitty.com/papers/arxiv:2112.03708)**. Sebastian Krinner, Nathan Lacroix, Ants Remm et al. · 2021 · Nature 605, 669 (2022) (arXiv:2112.03708 · doi:10.1038/s41586-022-04566-8 · 686 citations). Source: > Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments. In an error correction cycle… - **[State preservation by repetitive error detection in a superconducting quantum circuit](https://space-kitty.com/papers/arxiv:1411.7403)**. J. Kelly, R. Barends, Austin G. Fowler et al. · 2015 · Nature (arXiv:1411.7403 · doi:10.1038/nature14270 · 918 citations). Source: > Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors will not cause logical failure - a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here, we report the protection of classical state… - **[High-fidelity parallel entangling gates on a neutral-atom quantum computer](https://space-kitty.com/papers/arxiv:2304.05420)**. Simon J. Evered, Dolev Bluvstein, Marcin Kalinowski et al. · 2023 · Nature (arXiv:2304.05420 · doi:10.1038/s41586-023-06481-y · 521 citations). Source: > The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture. The major outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 a… - **[Bulk locality and quantum error correction in AdS/CFT](https://space-kitty.com/papers/arxiv:1411.7041)**. Ahmed Almheiri, Xi Dong, Daniel Harlow · 2015 · Journal of High Energy Physics (arXiv:1411.7041 · doi:10.1007/jhep04(2015)163 · 803 citations). Source: > We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme"… - **[High-threshold and low-overhead fault-tolerant quantum memory](https://space-kitty.com/papers/arxiv:2308.07915)**. Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta et al. · 2023 · Nature 627, 778-782 (2024) (arXiv:2308.07915 · doi:10.1038/s41586-024-07107-7 · 454 citations). Source: > Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The… - **[Fast universal quantum gate above the fault-tolerance threshold in silicon](https://space-kitty.com/papers/arxiv:2108.02626)**. Akito Noiri, Kenta Takeda, Takashi Nakajima et al. · 2022 · Nature (arXiv:2108.02626 · doi:10.1038/s41586-021-04182-y · 472 citations). Source: > Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to … - **[Surface code quantum computing by lattice surgery](https://space-kitty.com/papers/arxiv:1111.4022)**. Dominic C. Horsman, Austin G. Fowler, Simon J. Devitt et al. · 2012 · New Journal of Physics (arXiv:1111.4022 · doi:10.1088/1367-2630/14/12/123011 · 597 citations). Source: > In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correctio… - **[Realizing topologically ordered states on a quantum processor](https://space-kitty.com/papers/doi:10.1126/science.abi8378)**. Kevin J. Satzinger, Yu-Jie Liu, Adam Smith et al. · 2021 · Repository@Nottingham (University of Nottingham) (doi:10.1126/science.abi8378 · 426 citations). Source: > The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error-correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of -ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. … > _Abstract excerpt by Kevin J. Satzinger et al., CC-BY, https://doi.org/10.1126/science.abi8378; truncated._ - **[Demonstration of a quantum error detection code using a square lattice of four superconducting qubits](https://space-kitty.com/papers/arxiv:1410.6419)**. Antonio D. Corcoles, Easwar Magesan, Srikanth J. Srinivasan et al. · 2015 · Nature Communications (arXiv:1410.6419 · doi:10.1038/ncomms7979 · 489 citations). Source: > To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information encoded in the system. Stabilizer codes are attractive solutions to this problem, as they are analogous to classical linear codes, have simple and easily computed encoding networks, and allow efficient syndrome extraction. In these codes, syndrome extraction is performed via multi-qubit stabilizer measurements, which are bit and phase parity checks up to local… - **[Exponential suppression of bit or phase errors with cyclic error correction](https://space-kitty.com/papers/arxiv:2102.06132)**. Google Quantum AI, Zijun Chen, Kevin J. Satzinger et al. · 2021 · Nature (arXiv:2102.06132 · doi:10.1038/s41586-021-03588-y · 385 citations). Source: > Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold.… ## Newest - **[Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator](https://space-kitty.com/papers/arxiv:2610.36663)**. Shu He · 2026 (arXiv:2610.36663). Source: - **[Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes](https://space-kitty.com/papers/arxiv:2610.36700)**. Liangdong Lu, Ran Xu, Ruipan Yang et al. · 2026 (arXiv:2610.36700). Source: - **[Correlation-sensitive magic-state distillation from spin-squeezed neutral atoms](https://space-kitty.com/papers/arxiv:2610.36963)**. Ximo Wang, Ruyue Guo, Xinbo Li et al. · 2026 (arXiv:2610.36963). Source: - **[From QCCD Trapped-Ion Hardware to Quantum Compilers: Capabilities, Architectures, and Compilation](https://space-kitty.com/papers/arxiv:2610.36965)**. Ludwig Schmid, Jurek Eisinger, Daniel Schoenberger et al. · 2026 (arXiv:2610.36965). Source: - **[Measurement incompatibility and noiseless quantum codes](https://space-kitty.com/papers/arxiv:2610.37347)**. Yu-Xuan Zhang, Jing-Ling Chen · 2026 (arXiv:2610.37347). Source: - **[Self-Correcting 3D Surface Code with Growing Local Dimension](https://space-kitty.com/papers/arxiv:2610.35099)**. Jinkang Guo · 2026 (arXiv:2610.35099). Source: - **[A Control Line Multiplexing Framework for Scalable Quantum Computing](https://space-kitty.com/papers/arxiv:2610.35227)**. Dayu Li, Naibin Zhou, Zhiyuan Chen et al. · 2026 (arXiv:2610.35227). Source: - **[Multipartite dynamics beyond bipartite entanglement equilibration](https://space-kitty.com/papers/arxiv:2610.35377)**. Yan Liu, Ya-Wen Sun, Ren-Jie Ying et al. · 2026 (arXiv:2610.35377). Source: - **[Fast and accurate rare-event simulation by Markov chain Monte Carlo for general quantum codes](https://space-kitty.com/papers/arxiv:2610.35498)**. Junichi Haruna, Kotaro Murakami · 2026 (arXiv:2610.35498). Source: - **[Geometric aspects of fault tolerance](https://space-kitty.com/papers/arxiv:2610.35513)**. Jonathan Conrad · 2026 (arXiv:2610.35513). Source: --- Space Kitty Archive · https://space-kitty.com · API: https://space-kitty.com/api/v1 · MCP: https://space-kitty.com/mcp · Premium: $0.20/request via x402 (Base Sepolia (testnet)). Metadata: arXiv (CC0), OpenAlex (CC0), Europe PMC (CC BY/CC0 works), ClinicalTrials.gov.